Tentative seismic design guidelines for rocking structures
Many new and existing buildings have insufficient weight to resist overturning loads due to earthquakes without uplift. Previous versions of the New Zealand loadings code allowed simplified procedures for the design of rocking structures provided the ductility factor was limited to not more than two. The new loadings code, NZS 1170.5, removed this exemption and requires that a special study be performed whenever energy dissipation through rocking occurs. This paper presents a tentative design procedure intended to substitute for the special study required by the code.
The resistance function of rocking walls was developed from the principles of engineering mechanics. The results from a series of time history analyses were used to develop a procedure to estimate maximum seismic displacements and empirical equations were derived to estimate the dynamic amplification of inertia forces. A substitute structure approach, using spectral displacements at an effective period calculated from the ductility factor, provided accurate predictions of the displacements from more sophisticated nonlinear analyses.
Four example designs were completed and the predicted response compared to time history results. The procedure provided a satisfactory estimate of response for regular structures, but it was less accurate where torsional effects were significant.
Standards New Zealand, (1992). “Code of Practice for General Structural Design and Design Loadings for Buildings, NZS 4203:1992”, Standards New Zealand.
Standards New Zealand, (2002). “Structural Design Actions, Parts 5 Earthquake Actions – New Zealand, NZS1170.5:2004”, Standards New Zealand.
Huckelbridge, A. A. (1977), “Earthquake Simulation Tests of a Nine Story Steel Frame with Columns Allowed to Uplift”, Earthquake Engineering Research Center, Berkeley, CA, Report No. UCB/EERC-77-23.
Beck, J.L. and Skinner, R.I. (1974), “Seismic Response of a Reinforced Concrete Bridge Pier Designed to Step”, Earthquake Engineering & Structural Dynamics, Vol. 2 No. 4. DOI: https://doi.org/10.1002/eqe.4290020405
Priestley, M.J.N., Evison, R.J. and Carr, A.J. (1978), “Seismic Response of Structures Free to Rock on Their Foundations”, Bulletin of the New Zealand National Society for Earthquake Engineering, Vol. 11, No. 3, September.
ASCE, American Society of Civil Engineers, (2000), “Prestandard and Commentary for the Seismic Rehabilitation of Buildings”, Federal Emergency Management Agency FEMA-356, Washington, D.C.
Makris, N. and Konstantinidis, D. (2001), “The Rocking Spectrum and the Limitations of Design Guidelines”, PEER Report 2005/04 Pacific Earthquake Engineering Research Center College of Engineering University of California, Berkeley, August.
Kelly, T.E. (2008), “Development of Design Guidelines for Rocking Structures”, EQC Research Foundation Project OPR4, Holmes Consulting Group. DOI: https://doi.org/10.5459/bnzsee.42.4.239-274
Housner, G.W. (1963), “The behaviour of Inverted Pendulum Structures During Earthquakes”, Bulletin of the Seismological Society of America, Vol.53, No.2.
Yim, C.S., Chopra A.K. and Penzien, J. (1980), “Rocking Response Of Rigid Blocks To Earthquakes”, Earthquake Engineering and Structural Dynamics, Vol. 8, 565-587. DOI: https://doi.org/10.1002/eqe.4290080606
Ishiyama, Y. (1982), “Motions Of Rigid Bodies And Criteria For Overturning By Earthquake Excitations”, Earthquake Engineering and Structural Dynamics, Vol. 10, 635-650. DOI: https://doi.org/10.1002/eqe.4290100502
Psycharis, I. N. (1982), “Dynamic Behavior of Rocking Structures Allowed to Uplift”, EERL Report 81-02, California Institute of Technology, Pasadena, California.
Ma, Q., Wight, G.D., Butterworth, J. and Ingham, J.M. (2006), “Assessment of Current Procedures for Predicting the In-Plane Behaviour of Controlled Rocking Walls”, Proceedings of the 8th U.S. National Conference on Earthquake Engineering, San Francisco, California.
ElGawady, M.A., Ma, Q., Butterworth, J. and Ingham,J.M. (2006), “The Effect of Interface Material on the Dynamic Behaviour of Free Rocking Blocks”, Proceedings of the 8th U.S. National Conference on Earthquake Engineering, San Francisco, California.
Chung, M.A. and Larkin T.J. (2008), “Nonlinear Foundation Response of Liquid Storage Tanks under Seismic Loading”, Proceedings of New Zealand Society for Earthquake Engineering Annual Conference.
Toh, J.C.W. and Pender, M.J. (2008), “Earthquake Performance and Permanent Displacements of Shallow Foundations”, Proceedings of New Zealand National Society for Earthquake Engineering Annual Conference.
Harden, C., Hutchinson, T., Martin, G. and Kutter, B.L. (2005), “Numerical Modeling of the Nonlinear Cyclic Response of Shallow Foundations”, PEER Report 2005/04 Pacific Earthquake Engineering Research Center College of Engineering University of California, Berkeley, August.
Kutter, B.L., Martin, G., Hutchinson, T., Harden, C., Gajan, S. and Phalen, J. (2006), “Workshop on Modeling of Nonlinear Cyclic Load-Deformation Behavior of Shallow Foundations”, PEER Report 2005/14 Pacific Earthquake Engineering Research Center College of Engineering University of California, Berkeley, March.
Harden C.H. and Hutchinson, T. (2007), “Beam-on-Nonlinear-Winkler-Foundation Modeling of Shallow Rocking-Dominated Footings”, SEAOC 2007 Convention Proceedings.
Anderson, D.L. (2003), “Effect of Foundation Rocking on the Seismic Response of Shear Walls”, Canadian Journal of Civil Engineering, 30:360-365. DOI: https://doi.org/10.1139/l02-053
Mondkar, D.P. and Powell, G.H. (1979),”ANSR II Analysis of Non-linear Structural Response User's Manual”, EERC 79/17, University of California, Berkeley, July.
ATC (1996), “ATC Seismic Evaluation and Retrofit of Concrete Buildings”, Applied Technology Council, California.
Standards New Zealand, (1995). “Concrete Structures Standard Part 1 – The Design of Concrete Structures” also “Part 2 – Commentary”, NZS 3101:1995”, Standards New Zealand.
Kelly, T. E. (2007), “A Blind Prediction Test Of Nonlinear Analysis Procedures For Reinforced Concrete Shear Walls”, Bulletin of the New Zealand Society for Earthquake Engineering, Vol. 40, No. 3.
Copyright (c) 2009 Trevor E. Kelly
This work is licensed under a Creative Commons Attribution 4.0 International License.